Question

If $(1,1)$ and $(-3,5)$ are vertices of a diagonal of a square, then the equations of its sides through $(1,1)$ are

• A. $x-1=0$
• B. $x-y=0$
• C. $y-1=0$
• D. $x+y=0$

Answer 1

Answer: (A), (C)

The correct options are
A $x-1=0$
C $y-1=0$

Slope of diagonal will be $m=\frac{5-1}{-3-1}=-1$
Since, each side of a square makes ${45}^{\circ }$ angle with its diagonals, so the slope of sides will be
$\tan {45}^{\circ }=\left|\frac{-1-m_2}{1-m_2}\right|$
Case 1
$1=\frac{-1-m_2}{1-m_2}$
$\Rightarrow 1-m_2=-1-m_2$
Here $m_2$ is not defined so the line will be parallel to $y-$ axis
Line passing through point $(1,1)$ and parallel to $y-$ axis
$x=1$
Case 2
$1=\frac{1+m_2}{1-m_2}$
$\Rightarrow m_2=0$
Prallel to $x-$ axis
Line passing through point $(1,1)$ and parallel to $x-$ axis
​​​​​​​$y=1$